We investigate the Hermitian and the non-Hermitian dynamics of the mode entanglement in two identical optical cavities coupled by a chiral mirror. By employing the non-Hermitian quantum evolution, we calculate the logarithmic negativity measure of entanglement for initially Fock, coherent and squeezed states, separately. We verify the non-conservation of mean spin for the initially coherent and squeezed states when the coupling is non-reciprocal and report the associated spin noise for each case. We examine the effects of non-conserved symmetries on the mode correlations and determine the degree of non-reciprocal coupling to establish robust quantum entanglement.